For several decades, point-to-point wireless communications systems employed receive diversity based on antenna switching, equal-gain combining (EGC), or maximum-ratio combining (MRC). But with the development of cellular systems in the nineties, attention was turned to transmit diversity, which is more appropriate for the downlink.
The user terminal cost and power consumption considerations indeed favour transmit diversity with respect to receive diversity on the downlink, because this technique does not require the use of multiple antennas at user terminals.
The most well-known transmit diversity technique is the one introduced by Alamouti. This technique, which does not require any channel state information (CSI) at the transmitter side, has been included in most of the recently developed wireless communications systems standards including the IEEE 802.11n-2009 standard for Local Area Networks and the IEEE 802.16e-2005 standard, on which mobile WiMAX systems are based. Alamouti's transmit diversity leads to the same diversity order as the optimum receive diversity (MRC), but it loses 3 dB in terms of received signal-to-noise ratio (SNR) for the same total transmit power.
There are other transmit diversity options when the channel state information (CSI) is known either partially or fully at the transmitter side. One of these is the switching transmit diversity (STD).
In such a scheme, the channel is monitored through power measurements for the two transmit antennas and the best antenna is selected for transmission. STD loses some diversity gain with respect to MRC and Alamouti's transmit diversity, but it avoids the 3 dB loss of the Alamouti's technique in terms of SNR at the receiver. On the other hand, optimum transmit diversity (OTD) achieves the performance of MRC, but it requires the use of two transmit amplifiers each of which must be capable of transmitting the total transmit power. This leads to more costly transmitters.
For clarity, we now briefly describe the conventional spatial diversity techniques mentioned above.
The optimum spatial diversity technique at the receiver side is MRC, which can be described as follows for 2 receive antennas: Let hk1 and hk2 be the channel responses between the transmit antenna and the first and the second receive antenna, respectively. The signals received by the two receive antennas can be written as:rk1=hk1sk+nk1  (1.a)rk2=hk2sk+nk2  (1.b)where nk1 and nk2 are the additive noise terms. In MRC, the receiver computes:xk=h*k1rk1+h*k2rk2 =(|hk1|2+|hk2|2)sk+h*k1nk1+h*k2nk2  (2)
Symbol sk is detected by sending xk to a threshold detector. The signal-to-noise ratio (SNR) at the threshold detector input can be expressed asSNRk=(|hk1|2+|hk2|2)·SNR0  (3)where SNR0 is the power ratio of the transmitted symbols and the channel noise.
Next, optimum transmit diversity (OTD) consists of transmitting the data symbols such that the signals from the two transmit antennas arrive at the receiver in strictly identical phase and using optimum power loading.
More specifically, with hk1=|hk1|exp(jθ1) denoting the channel response between the first transmit antenna and the receive antenna, and hk2=|hk2|exp(jθ2) denoting the response between the second transmit antenna and the receive antenna, the signals transmitted by the two antennas are of the form:
                                          x                          k              ⁢                                                          ⁢              1                                =                                                                                      h                                      k                    ⁢                                                                                  ⁢                    1                                                                                                                                                                                                        h                                                  k                          ⁢                                                                                                          ⁢                          1                                                                                                            2                                    +                                                                                                          h                                                  k                          ⁢                                                                                                          ⁢                          2                                                                                                            2                                                                        ⁢                          s              k                                      ⁢                                  ⁢        and                            (                  4.          ⁢          a                )                                                      x                          k              ⁢                                                          ⁢              2                                =                                                                                                            h                                          k                      ⁢                                                                                          ⁢                      2                                                                                        ⁢                exp                ⁢                                                                  ⁢                                  j                  ⁡                                      (                                                                  θ                        1                                            -                                              θ                        2                                                              )                                                                                                                                                                                        h                                                  k                          ⁢                                                                                                          ⁢                          1                                                                                                            2                                    +                                                                                                          h                                                  k                          ⁢                                                                                                          ⁢                          2                                                                                                            2                                                                        ⁢                          s              k                                      ,                            (                  4.          ⁢          b                )            respectively. It can be easily verified that the SNR at the receiver is identical to that of MRC given by (3).
A diversity technique which comes close to OTD in terms of performance while avoiding the simultaneous use of multiple transmitters (which is cheaper) is known as switching transmit diversity (STD). Note that performance of switching diversity is the same whether switching is used at the transmitter or at the receiver. Focusing on STD at the transmit side, in the two transmit antenna case, the signal is transmitted from the first antenna if |hk1|≧|hk2| and it is transmitted from the second antenna otherwise. Then, the received signal can be written in the form:
                              r          k                =                  {                                                                                                                                        h                                                  k                          ⁢                                                                                                          ⁢                          1                                                                    ⁢                                              s                        k                                                              +                                          n                                              k                        ⁢                                                                                                  ⁢                        1                                                                              ,                                                                                                                        if                      ⁢                                                                                                                        ⁢                                                                                                                      ⁢                                                                                                h                                                      k                            ⁢                                                                                                                  ⁢                            1                                                                                                                                        ≥                                                                                        h                                                  k                          ⁢                                                                                                          ⁢                          2                                                                                                                            ⁢                                                                                                                                                                                                                                h                                                  k                          ⁢                                                                                                          ⁢                          2                                                                    ⁢                                              s                        k                                                              +                                          n                                              k                        ⁢                                                                                                  ⁢                        2                                                                              ,                                                                                                  if                    ⁢                                                                                  ⁢                                                                                        h                                                  k                          ⁢                                                                                                          ⁢                          1                                                                                                                            <                                                                                h                                              k                        ⁢                                                                                                  ⁢                        2                                                                                                                                                                        (        5        )            and the SNR at the threshold detector input becomes:
                              SNR          k                =                  {                                                                                                                                                              h                                                  k                          ⁢                                                                                                          ⁢                          1                                                                                                            2                                    ⁢                                      SNR                    0                                                                                                                    if                    ⁢                                                                                  ⁢                                                                                        h                                                  k                          ⁢                                                                                                          ⁢                          1                                                                                                                            ≥                                                                                h                                              k                        ⁢                                                                                                  ⁢                        2                                                                                                                                                                                                                                                                              h                                                  k                          ⁢                                                                                                          ⁢                          2                                                                                                            2                                    ⁢                                      SNR                    0                                                                                                                    if                    ⁢                                                                                  ⁢                                                                                        h                                                  k                          ⁢                                                                                                          ⁢                          1                                                                                                                            <                                                                                h                                              k                        ⁢                                                                                                  ⁢                        2                                                                                                                                                                        (        6        )            
It can be easily shown that, in terms of SNR, STD loses some 1.0-1.5 dB with respect to OTD.
A problem is that when no channel state information (CSI) is available at the transmitter side, OTD and STD cannot be implemented.
In that case, one may resort to Alamouti's transmit diversity. This technique leads to the same diversity performance as MRC and OTD, but it loses 3 dB in terms of SNR at the receiver, which is not desirable. This can be deduced by comparing (3) to the receiver SNR in Alamouti's transmit diversity which is given by:SNRk=(|hk1|2+|hk2|2)·SNR0/2  (7)